Timely inspection and deterrence

Abstract Verification of compliance to formal agreements requires the performance of routine inspections for detection of illegal behavior. Deterrence of violations is generally taken to be the primary objective of any verification regime. If the inspections are carried out in such a way that the gain the inspectee may expect from illegal behavior is smaller than that for behaving legally, then the inspections may indeed be said to have deterred violation. In this paper inspection problems characterized additionally by a `critical time' are considered for the first time in this context. The critical time is the maximum time interval within which illegal activity must be detected in order to meet the objectives of the agreement. Critically time-dependent inspection problems are modeled as two-person non-cooperative games between inspector and inspectee. They extend over a reference time interval in which the inspector performs by agreement precisely k inspections and in which the inspectee behaves illegally at most once. The inspections are assumed to incur statistical errors of the first and second kind, the former being detrimental to both protagonists. Variants for which the inspectee may or may not be in a position to take advantage of information gained during the reference time interval are considered. Equilibria are investigated and conditions for the existence of deterring inspection strategies are determined.